Drawing sheet metal blanks into three dimensional shapes is the established method of forming metal parts that are assembled to manufacture vehicles, appliances and other large products. Drawing operations are modeled by taking into account the physical properties of the blank and die set.
A simplified analytical formula that defines radial stresses for drawing a cylindrical cup is provided below:σ=(σy1n(R/r)+μQ/(πRt)+σyt/(4Rdie+2t))exp(μπ/2)
First Term Second Term Third Term Fourth Term—multiplier
Where:
σy—yield stress
R—radius of the flat blank at the beginning of the process
r—radius of the die at the entry to the cavity
μ—friction coefficient
Q—flange clamping force
π—3.14
t—sheet metal thickness
Rdie—radius of the edge of the die (usually 10 t or so)
Four major components identified as terms the 1st through fourth terms that make up the fundamentals of sheet metal drawing include:
First Term—plastic deformation of the flange
Second Term—friction between the die flange and the blank holder
Third Term—bending and unbending the sheet metal
Fourth Term—friction of the sheet metal with the die at the radius of the die entry
The first and third components are inherent in drawing operations and are generally unavoidable.
The second component relating to friction on the flange is minimized, or avoided, by employing the draw beads that force sheet metal to flow across the draw bead that creates tensile radial stresses. This technique is widely used today and allows sheet material drawing without clamping material on the entire flange. This approach minimizes the impact of the second component.
The fourth component is the friction of the sheet metal with the die at the radius of the die entry, and it has the most pronounced effect on the drawing process. The friction at the die entry is characterized as an exponential function. For example, if the fourth term friction coefficient is assumed to be 0.15, the multiplier is 1.29. If the friction coefficient is equal to the dry friction value (0.3 . . . 0.5), the multiplier is 1.57 . . . 2.17. Since the component defining plastic deformation of material in the flange is listed as ln(R/r), the ability to increase this term by 1.29 means that the ratio of R/r can be increased by exp(1.29)=3.65. Since height of the drawn cup is proportional to the surface of the flange (R2−r2), the increase of R more than factor of three makes a huge difference in the depth of draw. This effect is limited by bending-unbending term. Friction reduction makes a visible difference in the efficiency of the drawing operation. The fourth term is important for aluminum applications where a deep draw operation is required, such as door inner or fender applications.
Frictional forces limit the ability to draw sheet metal into the die cavity. Lightweight materials, such as aluminum alloys, require extending drawing limits to approach the ability to be drawn to the extent that is possible with mild steels.
Sheet metal part producers are developing lubrication technology to substantially reduce the coefficient of friction and increase the maximum draw depth. However, the most efficient lubrication systems often work in a narrow temperature window. As the temperature increases, the coefficient of friction increases. In high volume production conditions, especially when ambient temperatures are high, increased die temperatures are almost inevitable. Higher temperatures cause changes in drawing limits, and also changes the restraining forces that define wrinkling and spring back of parts after drawing.
This invention is directed to addressing the above problems and other problems that cause a reduction in drawing operation limits as summarized below.